Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.8% → 81.2%

Time: 26.8s

Alternatives: 22

Speedup: 0.5×

• 58.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
  (* j (- (* c t) (* i y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
  (* j (- (* c t) (* i y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 81.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot z - t \cdot a\\ t_3 := x \cdot t_2\\ t_4 := t \cdot c - y \cdot i\\ \mathbf{if}\;\left(t_3 + t_1\right) + j \cdot t_4 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(x, t_2, \mathsf{fma}\left(j, t_4, t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (- (* y z) (* t a)))
        (t_3 (* x t_2))
        (t_4 (- (* t c) (* y i))))
   (if (<= (+ (+ t_3 t_1) (* j t_4)) INFINITY)
     (fma x t_2 (fma j t_4 t_1))
     t_3)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = (y * z) - (t * a);
	double t_3 = x * t_2;
	double t_4 = (t * c) - (y * i);
	double tmp;
	if (((t_3 + t_1) + (j * t_4)) <= ((double) INFINITY)) {
		tmp = fma(x, t_2, fma(j, t_4, t_1));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(Float64(y * z) - Float64(t * a))
	t_3 = Float64(x * t_2)
	t_4 = Float64(Float64(t * c) - Float64(y * i))
	tmp = 0.0
	if (Float64(Float64(t_3 + t_1) + Float64(j * t_4)) <= Inf)
		tmp = fma(x, t_2, fma(j, t_4, t_1));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$3 + t$95$1), $MachinePrecision] + N[(j * t$95$4), $MachinePrecision]), $MachinePrecision], Infinity], N[(x * t$95$2 + N[(j * t$95$4 + t$95$1), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 92.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 92.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 92.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 92.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 92.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 92.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. *-commutative 92.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. *-commutative 92.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. distribute-rgt-neg-in 92.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      9. sub-neg 92.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      10. +-commutative 92.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(\left(-i \cdot a\right) + c \cdot z\right)}\right)\right)\right) \]

      11. distribute-neg-in 92.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)\right)}\right)\right) \]

      12. unsub-neg 92.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) - c \cdot z\right)}\right)\right) \]

      13. remove-double-neg 92.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right)\right)\right) \]

      14. *-commutative 92.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{a \cdot i} - c \cdot z\right)\right)\right) \]

      15. *-commutative 92.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right)\right)\right) \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - z \cdot c\right)\right)\right)} \]

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in x around inf 50.8%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - z \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 2: 81.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := \left(t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_2 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ (+ t_1 (* b (- (* a i) (* z c)))) (* j (- (* t c) (* y i))))))
   (if (<= t_2 INFINITY) t_2 t_1)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (t_1 + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (t_1 + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = (t_1 + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = (t_1 + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 92.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in x around inf 50.8%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 3: 52.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_4 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_5 := t_3 - c \cdot \left(z \cdot b\right)\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+91}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -3 \cdot 10^{+39}:\\ \;\;\;\;t_3 + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-137}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-292}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-196}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{-40}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+191}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* j (- (* t c) (* y i))))
        (t_4 (* a (- (* b i) (* x t))))
        (t_5 (- t_3 (* c (* z b)))))
   (if (<= a -1.55e+91)
     t_4
     (if (<= a -3e+39)
       (+ t_3 (* i (* a b)))
       (if (<= a -6e-18)
         t_2
         (if (<= a -3.7e-137)
           t_5
           (if (<= a -3e-214)
             t_1
             (if (<= a 2.1e-292)
               (* c (- (* t j) (* z b)))
               (if (<= a 4.5e-248)
                 t_1
                 (if (<= a 1.4e-196)
                   (* t (- (* c j) (* x a)))
                   (if (<= a 5e-110)
                     (+ (* x (* y z)) (* b (- (* a i) (* z c))))
                     (if (<= a 1.52e-40)
                       t_5
                       (if (<= a 2.95e+31)
                         t_2
                         (if (<= a 3.6e+191) t_5 t_4))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((t * c) - (y * i));
	double t_4 = a * ((b * i) - (x * t));
	double t_5 = t_3 - (c * (z * b));
	double tmp;
	if (a <= -1.55e+91) {
		tmp = t_4;
	} else if (a <= -3e+39) {
		tmp = t_3 + (i * (a * b));
	} else if (a <= -6e-18) {
		tmp = t_2;
	} else if (a <= -3.7e-137) {
		tmp = t_5;
	} else if (a <= -3e-214) {
		tmp = t_1;
	} else if (a <= 2.1e-292) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 4.5e-248) {
		tmp = t_1;
	} else if (a <= 1.4e-196) {
		tmp = t * ((c * j) - (x * a));
	} else if (a <= 5e-110) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (a <= 1.52e-40) {
		tmp = t_5;
	} else if (a <= 2.95e+31) {
		tmp = t_2;
	} else if (a <= 3.6e+191) {
		tmp = t_5;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = x * ((y * z) - (t * a))
    t_3 = j * ((t * c) - (y * i))
    t_4 = a * ((b * i) - (x * t))
    t_5 = t_3 - (c * (z * b))
    if (a <= (-1.55d+91)) then
        tmp = t_4
    else if (a <= (-3d+39)) then
        tmp = t_3 + (i * (a * b))
    else if (a <= (-6d-18)) then
        tmp = t_2
    else if (a <= (-3.7d-137)) then
        tmp = t_5
    else if (a <= (-3d-214)) then
        tmp = t_1
    else if (a <= 2.1d-292) then
        tmp = c * ((t * j) - (z * b))
    else if (a <= 4.5d-248) then
        tmp = t_1
    else if (a <= 1.4d-196) then
        tmp = t * ((c * j) - (x * a))
    else if (a <= 5d-110) then
        tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
    else if (a <= 1.52d-40) then
        tmp = t_5
    else if (a <= 2.95d+31) then
        tmp = t_2
    else if (a <= 3.6d+191) then
        tmp = t_5
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((t * c) - (y * i));
	double t_4 = a * ((b * i) - (x * t));
	double t_5 = t_3 - (c * (z * b));
	double tmp;
	if (a <= -1.55e+91) {
		tmp = t_4;
	} else if (a <= -3e+39) {
		tmp = t_3 + (i * (a * b));
	} else if (a <= -6e-18) {
		tmp = t_2;
	} else if (a <= -3.7e-137) {
		tmp = t_5;
	} else if (a <= -3e-214) {
		tmp = t_1;
	} else if (a <= 2.1e-292) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 4.5e-248) {
		tmp = t_1;
	} else if (a <= 1.4e-196) {
		tmp = t * ((c * j) - (x * a));
	} else if (a <= 5e-110) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (a <= 1.52e-40) {
		tmp = t_5;
	} else if (a <= 2.95e+31) {
		tmp = t_2;
	} else if (a <= 3.6e+191) {
		tmp = t_5;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = x * ((y * z) - (t * a))
	t_3 = j * ((t * c) - (y * i))
	t_4 = a * ((b * i) - (x * t))
	t_5 = t_3 - (c * (z * b))
	tmp = 0
	if a <= -1.55e+91:
		tmp = t_4
	elif a <= -3e+39:
		tmp = t_3 + (i * (a * b))
	elif a <= -6e-18:
		tmp = t_2
	elif a <= -3.7e-137:
		tmp = t_5
	elif a <= -3e-214:
		tmp = t_1
	elif a <= 2.1e-292:
		tmp = c * ((t * j) - (z * b))
	elif a <= 4.5e-248:
		tmp = t_1
	elif a <= 1.4e-196:
		tmp = t * ((c * j) - (x * a))
	elif a <= 5e-110:
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
	elif a <= 1.52e-40:
		tmp = t_5
	elif a <= 2.95e+31:
		tmp = t_2
	elif a <= 3.6e+191:
		tmp = t_5
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_4 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_5 = Float64(t_3 - Float64(c * Float64(z * b)))
	tmp = 0.0
	if (a <= -1.55e+91)
		tmp = t_4;
	elseif (a <= -3e+39)
		tmp = Float64(t_3 + Float64(i * Float64(a * b)));
	elseif (a <= -6e-18)
		tmp = t_2;
	elseif (a <= -3.7e-137)
		tmp = t_5;
	elseif (a <= -3e-214)
		tmp = t_1;
	elseif (a <= 2.1e-292)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (a <= 4.5e-248)
		tmp = t_1;
	elseif (a <= 1.4e-196)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (a <= 5e-110)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (a <= 1.52e-40)
		tmp = t_5;
	elseif (a <= 2.95e+31)
		tmp = t_2;
	elseif (a <= 3.6e+191)
		tmp = t_5;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = x * ((y * z) - (t * a));
	t_3 = j * ((t * c) - (y * i));
	t_4 = a * ((b * i) - (x * t));
	t_5 = t_3 - (c * (z * b));
	tmp = 0.0;
	if (a <= -1.55e+91)
		tmp = t_4;
	elseif (a <= -3e+39)
		tmp = t_3 + (i * (a * b));
	elseif (a <= -6e-18)
		tmp = t_2;
	elseif (a <= -3.7e-137)
		tmp = t_5;
	elseif (a <= -3e-214)
		tmp = t_1;
	elseif (a <= 2.1e-292)
		tmp = c * ((t * j) - (z * b));
	elseif (a <= 4.5e-248)
		tmp = t_1;
	elseif (a <= 1.4e-196)
		tmp = t * ((c * j) - (x * a));
	elseif (a <= 5e-110)
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	elseif (a <= 1.52e-40)
		tmp = t_5;
	elseif (a <= 2.95e+31)
		tmp = t_2;
	elseif (a <= 3.6e+191)
		tmp = t_5;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.55e+91], t$95$4, If[LessEqual[a, -3e+39], N[(t$95$3 + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6e-18], t$95$2, If[LessEqual[a, -3.7e-137], t$95$5, If[LessEqual[a, -3e-214], t$95$1, If[LessEqual[a, 2.1e-292], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e-248], t$95$1, If[LessEqual[a, 1.4e-196], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-110], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.52e-40], t$95$5, If[LessEqual[a, 2.95e+31], t$95$2, If[LessEqual[a, 3.6e+191], t$95$5, t$95$4]]]]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -1.54999999999999999e91 or 3.5999999999999999e191 < a

   1. Initial program 62.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 62.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 62.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 62.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 62.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 62.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 62.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 62.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 62.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 76.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 76.7%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 76.7%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 76.7%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 76.7%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 76.7%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 76.7%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 76.7%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   if -1.54999999999999999e91 < a < -3e39

   1. Initial program 71.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 79.9%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. *-commutative 79.9%

         \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot a} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. associate-*r* 79.9%

         \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 79.9%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   if -3e39 < a < -5.99999999999999966e-18 or 1.51999999999999992e-40 < a < 2.9500000000000002e31

   1. Initial program 67.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 67.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 67.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 67.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 67.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 67.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 67.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 67.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 67.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in x around inf 71.2%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if -5.99999999999999966e-18 < a < -3.7e-137 or 5e-110 < a < 1.51999999999999992e-40 or 2.9500000000000002e31 < a < 3.5999999999999999e191

   1. Initial program 79.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 79.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 79.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 79.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 79.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 79.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 79.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 79.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 72.7%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 72.7%

         \[\leadsto \color{blue}{\left(-c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 72.7%

      \[\leadsto \color{blue}{\left(-c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   if -3.7e-137 < a < -2.99999999999999994e-214 or 2.09999999999999989e-292 < a < 4.4999999999999996e-248

   1. Initial program 70.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 70.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 70.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 70.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 83.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 83.2%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 83.2%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 83.2%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 83.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -2.99999999999999994e-214 < a < 2.09999999999999989e-292

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 80.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 80.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 80.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 85.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if 4.4999999999999996e-248 < a < 1.3999999999999999e-196

   1. Initial program 66.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 66.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 66.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 66.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 66.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 66.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 66.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 66.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 78.2%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 78.2%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 78.2%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 78.2%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 78.2%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if 1.3999999999999999e-196 < a < 5e-110

   1. Initial program 58.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 58.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 58.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 58.2%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 58.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 58.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 58.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 58.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 58.8%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in y around inf 52.3%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b \]
   6. Step-by-step derivation

      1. *-commutative 52.3%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b \]

   7. Simplified 52.3%

      \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b \]
3. Recombined 8 regimes into one program.

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+91}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{+39}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-18}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-137}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-214}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-292}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-248}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-196}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.52 \cdot 10^{-40}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+191}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 4: 54.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_4 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_5 := t_3 - c \cdot \left(z \cdot b\right)\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{+88}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -5 \cdot 10^{+40}:\\ \;\;\;\;t_3 + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-137}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-216}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-292}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-40}:\\ \;\;\;\;t_3 - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+191}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* j (- (* t c) (* y i))))
        (t_4 (* a (- (* b i) (* x t))))
        (t_5 (- t_3 (* c (* z b)))))
   (if (<= a -3.3e+88)
     t_4
     (if (<= a -5e+40)
       (+ t_3 (* i (* a b)))
       (if (<= a -4.2e-13)
         t_2
         (if (<= a -1.05e-137)
           t_5
           (if (<= a -6.2e-216)
             t_1
             (if (<= a 1.55e-292)
               (* c (- (* t j) (* z b)))
               (if (<= a 3.5e-255)
                 t_1
                 (if (<= a 3.6e-40)
                   (- t_3 (* z (* b c)))
                   (if (<= a 2.6e+31)
                     t_2
                     (if (<= a 4.2e+191) t_5 t_4))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((t * c) - (y * i));
	double t_4 = a * ((b * i) - (x * t));
	double t_5 = t_3 - (c * (z * b));
	double tmp;
	if (a <= -3.3e+88) {
		tmp = t_4;
	} else if (a <= -5e+40) {
		tmp = t_3 + (i * (a * b));
	} else if (a <= -4.2e-13) {
		tmp = t_2;
	} else if (a <= -1.05e-137) {
		tmp = t_5;
	} else if (a <= -6.2e-216) {
		tmp = t_1;
	} else if (a <= 1.55e-292) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 3.5e-255) {
		tmp = t_1;
	} else if (a <= 3.6e-40) {
		tmp = t_3 - (z * (b * c));
	} else if (a <= 2.6e+31) {
		tmp = t_2;
	} else if (a <= 4.2e+191) {
		tmp = t_5;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = x * ((y * z) - (t * a))
    t_3 = j * ((t * c) - (y * i))
    t_4 = a * ((b * i) - (x * t))
    t_5 = t_3 - (c * (z * b))
    if (a <= (-3.3d+88)) then
        tmp = t_4
    else if (a <= (-5d+40)) then
        tmp = t_3 + (i * (a * b))
    else if (a <= (-4.2d-13)) then
        tmp = t_2
    else if (a <= (-1.05d-137)) then
        tmp = t_5
    else if (a <= (-6.2d-216)) then
        tmp = t_1
    else if (a <= 1.55d-292) then
        tmp = c * ((t * j) - (z * b))
    else if (a <= 3.5d-255) then
        tmp = t_1
    else if (a <= 3.6d-40) then
        tmp = t_3 - (z * (b * c))
    else if (a <= 2.6d+31) then
        tmp = t_2
    else if (a <= 4.2d+191) then
        tmp = t_5
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((t * c) - (y * i));
	double t_4 = a * ((b * i) - (x * t));
	double t_5 = t_3 - (c * (z * b));
	double tmp;
	if (a <= -3.3e+88) {
		tmp = t_4;
	} else if (a <= -5e+40) {
		tmp = t_3 + (i * (a * b));
	} else if (a <= -4.2e-13) {
		tmp = t_2;
	} else if (a <= -1.05e-137) {
		tmp = t_5;
	} else if (a <= -6.2e-216) {
		tmp = t_1;
	} else if (a <= 1.55e-292) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 3.5e-255) {
		tmp = t_1;
	} else if (a <= 3.6e-40) {
		tmp = t_3 - (z * (b * c));
	} else if (a <= 2.6e+31) {
		tmp = t_2;
	} else if (a <= 4.2e+191) {
		tmp = t_5;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = x * ((y * z) - (t * a))
	t_3 = j * ((t * c) - (y * i))
	t_4 = a * ((b * i) - (x * t))
	t_5 = t_3 - (c * (z * b))
	tmp = 0
	if a <= -3.3e+88:
		tmp = t_4
	elif a <= -5e+40:
		tmp = t_3 + (i * (a * b))
	elif a <= -4.2e-13:
		tmp = t_2
	elif a <= -1.05e-137:
		tmp = t_5
	elif a <= -6.2e-216:
		tmp = t_1
	elif a <= 1.55e-292:
		tmp = c * ((t * j) - (z * b))
	elif a <= 3.5e-255:
		tmp = t_1
	elif a <= 3.6e-40:
		tmp = t_3 - (z * (b * c))
	elif a <= 2.6e+31:
		tmp = t_2
	elif a <= 4.2e+191:
		tmp = t_5
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_4 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_5 = Float64(t_3 - Float64(c * Float64(z * b)))
	tmp = 0.0
	if (a <= -3.3e+88)
		tmp = t_4;
	elseif (a <= -5e+40)
		tmp = Float64(t_3 + Float64(i * Float64(a * b)));
	elseif (a <= -4.2e-13)
		tmp = t_2;
	elseif (a <= -1.05e-137)
		tmp = t_5;
	elseif (a <= -6.2e-216)
		tmp = t_1;
	elseif (a <= 1.55e-292)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (a <= 3.5e-255)
		tmp = t_1;
	elseif (a <= 3.6e-40)
		tmp = Float64(t_3 - Float64(z * Float64(b * c)));
	elseif (a <= 2.6e+31)
		tmp = t_2;
	elseif (a <= 4.2e+191)
		tmp = t_5;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = x * ((y * z) - (t * a));
	t_3 = j * ((t * c) - (y * i));
	t_4 = a * ((b * i) - (x * t));
	t_5 = t_3 - (c * (z * b));
	tmp = 0.0;
	if (a <= -3.3e+88)
		tmp = t_4;
	elseif (a <= -5e+40)
		tmp = t_3 + (i * (a * b));
	elseif (a <= -4.2e-13)
		tmp = t_2;
	elseif (a <= -1.05e-137)
		tmp = t_5;
	elseif (a <= -6.2e-216)
		tmp = t_1;
	elseif (a <= 1.55e-292)
		tmp = c * ((t * j) - (z * b));
	elseif (a <= 3.5e-255)
		tmp = t_1;
	elseif (a <= 3.6e-40)
		tmp = t_3 - (z * (b * c));
	elseif (a <= 2.6e+31)
		tmp = t_2;
	elseif (a <= 4.2e+191)
		tmp = t_5;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.3e+88], t$95$4, If[LessEqual[a, -5e+40], N[(t$95$3 + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.2e-13], t$95$2, If[LessEqual[a, -1.05e-137], t$95$5, If[LessEqual[a, -6.2e-216], t$95$1, If[LessEqual[a, 1.55e-292], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.5e-255], t$95$1, If[LessEqual[a, 3.6e-40], N[(t$95$3 - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e+31], t$95$2, If[LessEqual[a, 4.2e+191], t$95$5, t$95$4]]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -3.3000000000000003e88 or 4.2000000000000001e191 < a

   1. Initial program 62.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 62.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 62.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 62.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 62.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 62.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 62.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 62.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 62.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 76.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 76.7%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 76.7%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 76.7%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 76.7%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 76.7%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 76.7%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 76.7%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   if -3.3000000000000003e88 < a < -5.00000000000000003e40

   1. Initial program 71.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 79.9%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. *-commutative 79.9%

         \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot a} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. associate-*r* 79.9%

         \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 79.9%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   if -5.00000000000000003e40 < a < -4.19999999999999977e-13 or 3.6e-40 < a < 2.6e31

   1. Initial program 67.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 67.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 67.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 67.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 67.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 67.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 67.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 67.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 67.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in x around inf 71.2%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if -4.19999999999999977e-13 < a < -1.04999999999999996e-137 or 2.6e31 < a < 4.2000000000000001e191

   1. Initial program 78.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 78.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 78.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 78.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 78.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 78.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 78.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 78.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 72.3%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 72.3%

         \[\leadsto \color{blue}{\left(-c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 72.3%

      \[\leadsto \color{blue}{\left(-c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   if -1.04999999999999996e-137 < a < -6.2000000000000004e-216 or 1.55e-292 < a < 3.49999999999999979e-255

   1. Initial program 67.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 67.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 67.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 67.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 67.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 67.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 67.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 67.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 67.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 86.0%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 86.0%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 86.0%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 86.0%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 86.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -6.2000000000000004e-216 < a < 1.55e-292

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 80.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 80.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 80.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 80.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 85.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if 3.49999999999999979e-255 < a < 3.6e-40

   1. Initial program 71.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 55.4%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 55.4%

         \[\leadsto \color{blue}{\left(-c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. associate-*r* 57.8%

         \[\leadsto \left(-\color{blue}{\left(c \cdot b\right) \cdot z}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. distribute-lft-neg-in 57.8%

         \[\leadsto \color{blue}{\left(-c \cdot b\right) \cdot z} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. distribute-rgt-neg-in 57.8%

         \[\leadsto \color{blue}{\left(c \cdot \left(-b\right)\right)} \cdot z + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 57.8%

      \[\leadsto \color{blue}{\left(c \cdot \left(-b\right)\right) \cdot z} + j \cdot \left(t \cdot c - y \cdot i\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{+88}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{+40}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-137}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-216}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-292}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-255}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-40}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+191}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 5: 57.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot t\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := t_2 - t_1\\ t_4 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_5 := x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;t \leq -2.05 \cdot 10^{+67}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -70000000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-8}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - t_1\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-48}:\\ \;\;\;\;t_2 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-84}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-183}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-57}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 240:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{+112}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x t)))
        (t_2 (* j (- (* t c) (* y i))))
        (t_3 (- t_2 t_1))
        (t_4 (* t (- (* c j) (* x a))))
        (t_5 (+ (* x (* y z)) (* b (- (* a i) (* z c))))))
   (if (<= t -2.05e+67)
     t_4
     (if (<= t -70000000.0)
       (* z (- (* x y) (* b c)))
       (if (<= t -5.1e-8)
         (- (* i (* a b)) t_1)
         (if (<= t -2.6e-48)
           (- t_2 (* c (* z b)))
           (if (<= t -5.5e-84)
             (* a (- (* b i) (* x t)))
             (if (<= t -2.45e-183)
               t_3
               (if (<= t 1.08e-57)
                 t_5
                 (if (<= t 240.0) t_3 (if (<= t 2.75e+112) t_5 t_4)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * t);
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = t_2 - t_1;
	double t_4 = t * ((c * j) - (x * a));
	double t_5 = (x * (y * z)) + (b * ((a * i) - (z * c)));
	double tmp;
	if (t <= -2.05e+67) {
		tmp = t_4;
	} else if (t <= -70000000.0) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= -5.1e-8) {
		tmp = (i * (a * b)) - t_1;
	} else if (t <= -2.6e-48) {
		tmp = t_2 - (c * (z * b));
	} else if (t <= -5.5e-84) {
		tmp = a * ((b * i) - (x * t));
	} else if (t <= -2.45e-183) {
		tmp = t_3;
	} else if (t <= 1.08e-57) {
		tmp = t_5;
	} else if (t <= 240.0) {
		tmp = t_3;
	} else if (t <= 2.75e+112) {
		tmp = t_5;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = a * (x * t)
    t_2 = j * ((t * c) - (y * i))
    t_3 = t_2 - t_1
    t_4 = t * ((c * j) - (x * a))
    t_5 = (x * (y * z)) + (b * ((a * i) - (z * c)))
    if (t <= (-2.05d+67)) then
        tmp = t_4
    else if (t <= (-70000000.0d0)) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= (-5.1d-8)) then
        tmp = (i * (a * b)) - t_1
    else if (t <= (-2.6d-48)) then
        tmp = t_2 - (c * (z * b))
    else if (t <= (-5.5d-84)) then
        tmp = a * ((b * i) - (x * t))
    else if (t <= (-2.45d-183)) then
        tmp = t_3
    else if (t <= 1.08d-57) then
        tmp = t_5
    else if (t <= 240.0d0) then
        tmp = t_3
    else if (t <= 2.75d+112) then
        tmp = t_5
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * t);
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = t_2 - t_1;
	double t_4 = t * ((c * j) - (x * a));
	double t_5 = (x * (y * z)) + (b * ((a * i) - (z * c)));
	double tmp;
	if (t <= -2.05e+67) {
		tmp = t_4;
	} else if (t <= -70000000.0) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= -5.1e-8) {
		tmp = (i * (a * b)) - t_1;
	} else if (t <= -2.6e-48) {
		tmp = t_2 - (c * (z * b));
	} else if (t <= -5.5e-84) {
		tmp = a * ((b * i) - (x * t));
	} else if (t <= -2.45e-183) {
		tmp = t_3;
	} else if (t <= 1.08e-57) {
		tmp = t_5;
	} else if (t <= 240.0) {
		tmp = t_3;
	} else if (t <= 2.75e+112) {
		tmp = t_5;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * t)
	t_2 = j * ((t * c) - (y * i))
	t_3 = t_2 - t_1
	t_4 = t * ((c * j) - (x * a))
	t_5 = (x * (y * z)) + (b * ((a * i) - (z * c)))
	tmp = 0
	if t <= -2.05e+67:
		tmp = t_4
	elif t <= -70000000.0:
		tmp = z * ((x * y) - (b * c))
	elif t <= -5.1e-8:
		tmp = (i * (a * b)) - t_1
	elif t <= -2.6e-48:
		tmp = t_2 - (c * (z * b))
	elif t <= -5.5e-84:
		tmp = a * ((b * i) - (x * t))
	elif t <= -2.45e-183:
		tmp = t_3
	elif t <= 1.08e-57:
		tmp = t_5
	elif t <= 240.0:
		tmp = t_3
	elif t <= 2.75e+112:
		tmp = t_5
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * t))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_3 = Float64(t_2 - t_1)
	t_4 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_5 = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	tmp = 0.0
	if (t <= -2.05e+67)
		tmp = t_4;
	elseif (t <= -70000000.0)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= -5.1e-8)
		tmp = Float64(Float64(i * Float64(a * b)) - t_1);
	elseif (t <= -2.6e-48)
		tmp = Float64(t_2 - Float64(c * Float64(z * b)));
	elseif (t <= -5.5e-84)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (t <= -2.45e-183)
		tmp = t_3;
	elseif (t <= 1.08e-57)
		tmp = t_5;
	elseif (t <= 240.0)
		tmp = t_3;
	elseif (t <= 2.75e+112)
		tmp = t_5;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (x * t);
	t_2 = j * ((t * c) - (y * i));
	t_3 = t_2 - t_1;
	t_4 = t * ((c * j) - (x * a));
	t_5 = (x * (y * z)) + (b * ((a * i) - (z * c)));
	tmp = 0.0;
	if (t <= -2.05e+67)
		tmp = t_4;
	elseif (t <= -70000000.0)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= -5.1e-8)
		tmp = (i * (a * b)) - t_1;
	elseif (t <= -2.6e-48)
		tmp = t_2 - (c * (z * b));
	elseif (t <= -5.5e-84)
		tmp = a * ((b * i) - (x * t));
	elseif (t <= -2.45e-183)
		tmp = t_3;
	elseif (t <= 1.08e-57)
		tmp = t_5;
	elseif (t <= 240.0)
		tmp = t_3;
	elseif (t <= 2.75e+112)
		tmp = t_5;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.05e+67], t$95$4, If[LessEqual[t, -70000000.0], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.1e-8], N[(N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, -2.6e-48], N[(t$95$2 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.5e-84], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.45e-183], t$95$3, If[LessEqual[t, 1.08e-57], t$95$5, If[LessEqual[t, 240.0], t$95$3, If[LessEqual[t, 2.75e+112], t$95$5, t$95$4]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -2.0499999999999999e67 or 2.75000000000000013e112 < t

   1. Initial program 58.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 58.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 58.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 58.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 58.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 58.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 58.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 58.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 58.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 70.2%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 70.2%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 70.2%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 70.2%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 70.2%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -2.0499999999999999e67 < t < -7e7

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 66.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 66.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 66.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 66.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 66.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 66.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 66.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 66.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 63.2%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   if -7e7 < t < -5.10000000000000001e-8

   1. Initial program 100.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 100.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 100.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 100.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 100.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 100.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 100.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 100.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 68.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 68.3%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 68.3%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 68.3%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 68.3%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 68.3%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 68.3%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 68.3%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   7. Taylor expanded in b around 0 100.0%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]

   if -5.10000000000000001e-8 < t < -2.59999999999999987e-48

   1. Initial program 72.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 72.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 72.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 72.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 72.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 72.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 72.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 72.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 72.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 87.3%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 87.3%

         \[\leadsto \color{blue}{\left(-c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 87.3%

      \[\leadsto \color{blue}{\left(-c \cdot \left(b \cdot z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   if -2.59999999999999987e-48 < t < -5.50000000000000019e-84

   1. Initial program 69.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 69.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 69.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 69.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 69.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 69.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 69.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 69.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 69.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 80.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 80.1%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 80.1%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 80.1%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 80.1%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 80.1%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 80.1%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 80.1%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   if -5.50000000000000019e-84 < t < -2.45e-183 or 1.08e-57 < t < 240

   1. Initial program 78.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 78.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 78.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 78.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 78.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 78.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 78.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 78.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 68.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 68.2%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 68.2%

         \[\leadsto \left(-\color{blue}{\left(t \cdot x\right) \cdot a}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. distribute-rgt-neg-in 68.2%

         \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 68.2%

      \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   if -2.45e-183 < t < 1.08e-57 or 240 < t < 2.75000000000000013e112

   1. Initial program 77.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 80.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 80.2%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 80.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 80.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 80.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 80.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 73.7%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in y around inf 71.7%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b \]
   6. Step-by-step derivation

      1. *-commutative 71.7%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b \]

   7. Simplified 71.7%

      \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b \]
3. Recombined 7 regimes into one program.

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+67}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -70000000:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-8}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-48}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-84}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq -2.45 \cdot 10^{-183}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 240:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{+112}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 6: 53.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_4 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+66}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-152}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-89}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-55}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+112}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* i (* a b))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (* t (- (* c j) (* x a))))
        (t_4 (* b (- (* a i) (* z c)))))
   (if (<= t -3.2e+66)
     t_3
     (if (<= t -2.4e-41)
       t_2
       (if (<= t -1.55e-183)
         t_1
         (if (<= t 7.5e-152)
           t_4
           (if (<= t 1.85e-89)
             (* y (- (* x z) (* i j)))
             (if (<= t 4.9e-55)
               t_4
               (if (<= t 6.5e+46) t_1 (if (<= t 2.25e+112) t_2 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (i * (a * b));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((c * j) - (x * a));
	double t_4 = b * ((a * i) - (z * c));
	double tmp;
	if (t <= -3.2e+66) {
		tmp = t_3;
	} else if (t <= -2.4e-41) {
		tmp = t_2;
	} else if (t <= -1.55e-183) {
		tmp = t_1;
	} else if (t <= 7.5e-152) {
		tmp = t_4;
	} else if (t <= 1.85e-89) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 4.9e-55) {
		tmp = t_4;
	} else if (t <= 6.5e+46) {
		tmp = t_1;
	} else if (t <= 2.25e+112) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (j * ((t * c) - (y * i))) + (i * (a * b))
    t_2 = z * ((x * y) - (b * c))
    t_3 = t * ((c * j) - (x * a))
    t_4 = b * ((a * i) - (z * c))
    if (t <= (-3.2d+66)) then
        tmp = t_3
    else if (t <= (-2.4d-41)) then
        tmp = t_2
    else if (t <= (-1.55d-183)) then
        tmp = t_1
    else if (t <= 7.5d-152) then
        tmp = t_4
    else if (t <= 1.85d-89) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= 4.9d-55) then
        tmp = t_4
    else if (t <= 6.5d+46) then
        tmp = t_1
    else if (t <= 2.25d+112) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (i * (a * b));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((c * j) - (x * a));
	double t_4 = b * ((a * i) - (z * c));
	double tmp;
	if (t <= -3.2e+66) {
		tmp = t_3;
	} else if (t <= -2.4e-41) {
		tmp = t_2;
	} else if (t <= -1.55e-183) {
		tmp = t_1;
	} else if (t <= 7.5e-152) {
		tmp = t_4;
	} else if (t <= 1.85e-89) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 4.9e-55) {
		tmp = t_4;
	} else if (t <= 6.5e+46) {
		tmp = t_1;
	} else if (t <= 2.25e+112) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (i * (a * b))
	t_2 = z * ((x * y) - (b * c))
	t_3 = t * ((c * j) - (x * a))
	t_4 = b * ((a * i) - (z * c))
	tmp = 0
	if t <= -3.2e+66:
		tmp = t_3
	elif t <= -2.4e-41:
		tmp = t_2
	elif t <= -1.55e-183:
		tmp = t_1
	elif t <= 7.5e-152:
		tmp = t_4
	elif t <= 1.85e-89:
		tmp = y * ((x * z) - (i * j))
	elif t <= 4.9e-55:
		tmp = t_4
	elif t <= 6.5e+46:
		tmp = t_1
	elif t <= 2.25e+112:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(i * Float64(a * b)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_4 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (t <= -3.2e+66)
		tmp = t_3;
	elseif (t <= -2.4e-41)
		tmp = t_2;
	elseif (t <= -1.55e-183)
		tmp = t_1;
	elseif (t <= 7.5e-152)
		tmp = t_4;
	elseif (t <= 1.85e-89)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= 4.9e-55)
		tmp = t_4;
	elseif (t <= 6.5e+46)
		tmp = t_1;
	elseif (t <= 2.25e+112)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) + (i * (a * b));
	t_2 = z * ((x * y) - (b * c));
	t_3 = t * ((c * j) - (x * a));
	t_4 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (t <= -3.2e+66)
		tmp = t_3;
	elseif (t <= -2.4e-41)
		tmp = t_2;
	elseif (t <= -1.55e-183)
		tmp = t_1;
	elseif (t <= 7.5e-152)
		tmp = t_4;
	elseif (t <= 1.85e-89)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= 4.9e-55)
		tmp = t_4;
	elseif (t <= 6.5e+46)
		tmp = t_1;
	elseif (t <= 2.25e+112)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.2e+66], t$95$3, If[LessEqual[t, -2.4e-41], t$95$2, If[LessEqual[t, -1.55e-183], t$95$1, If[LessEqual[t, 7.5e-152], t$95$4, If[LessEqual[t, 1.85e-89], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.9e-55], t$95$4, If[LessEqual[t, 6.5e+46], t$95$1, If[LessEqual[t, 2.25e+112], t$95$2, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.2e66 or 2.24999999999999995e112 < t

   1. Initial program 58.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 58.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 58.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 58.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 58.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 58.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 58.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 58.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 58.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 70.2%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 70.2%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 70.2%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 70.2%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 70.2%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -3.2e66 < t < -2.40000000000000022e-41 or 6.50000000000000008e46 < t < 2.24999999999999995e112

   1. Initial program 67.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 67.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 67.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 67.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 67.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 67.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 67.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 67.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 67.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 66.5%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   if -2.40000000000000022e-41 < t < -1.55e-183 or 4.90000000000000035e-55 < t < 6.50000000000000008e46

   1. Initial program 78.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 78.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 63.7%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. *-commutative 63.7%

         \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot a} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. associate-*r* 65.4%

         \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 65.4%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   if -1.55e-183 < t < 7.5e-152 or 1.8499999999999999e-89 < t < 4.90000000000000035e-55

   1. Initial program 81.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 81.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 81.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 81.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 81.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 81.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 81.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 81.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 81.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 68.9%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   if 7.5e-152 < t < 1.8499999999999999e-89

   1. Initial program 75.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 75.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 75.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 68.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 68.4%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 68.4%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 68.4%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 68.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-41}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-183}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-152}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-89}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+46}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{+112}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 7: 61.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -6.6 \cdot 10^{+79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.25 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-175}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c)))))
        (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -6.6e+79)
     t_2
     (if (<= c -2.25e-277)
       t_1
       (if (<= c 5e-175)
         (* i (- (* a b) (* y j)))
         (if (<= c 2.5e+71) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -6.6e+79) {
		tmp = t_2;
	} else if (c <= -2.25e-277) {
		tmp = t_1;
	} else if (c <= 5e-175) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 2.5e+71) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-6.6d+79)) then
        tmp = t_2
    else if (c <= (-2.25d-277)) then
        tmp = t_1
    else if (c <= 5d-175) then
        tmp = i * ((a * b) - (y * j))
    else if (c <= 2.5d+71) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -6.6e+79) {
		tmp = t_2;
	} else if (c <= -2.25e-277) {
		tmp = t_1;
	} else if (c <= 5e-175) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 2.5e+71) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -6.6e+79:
		tmp = t_2
	elif c <= -2.25e-277:
		tmp = t_1
	elif c <= 5e-175:
		tmp = i * ((a * b) - (y * j))
	elif c <= 2.5e+71:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -6.6e+79)
		tmp = t_2;
	elseif (c <= -2.25e-277)
		tmp = t_1;
	elseif (c <= 5e-175)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (c <= 2.5e+71)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -6.6e+79)
		tmp = t_2;
	elseif (c <= -2.25e-277)
		tmp = t_1;
	elseif (c <= 5e-175)
		tmp = i * ((a * b) - (y * j));
	elseif (c <= 2.5e+71)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.6e+79], t$95$2, If[LessEqual[c, -2.25e-277], t$95$1, If[LessEqual[c, 5e-175], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.5e+71], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.6000000000000003e79 or 2.49999999999999986e71 < c

   1. Initial program 59.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 59.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 59.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 59.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 59.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 59.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 59.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 59.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 59.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 69.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if -6.6000000000000003e79 < c < -2.24999999999999996e-277 or 5e-175 < c < 2.49999999999999986e71

   1. Initial program 77.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 79.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 79.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 79.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 72.3%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   if -2.24999999999999996e-277 < c < 5e-175

   1. Initial program 78.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 78.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 78.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 78.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 78.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 78.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 78.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 78.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 69.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(a \cdot b\right)\right) \cdot i} \]
   5. Step-by-step derivation

      1. *-commutative 69.4%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(y \cdot j\right) - -1 \cdot \left(a \cdot b\right)\right)} \]

      2. associate-*r* 69.4%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-1 \cdot a\right) \cdot b}\right) \]

      3. neg-mul-1 69.4%

         \[\leadsto i \cdot \left(-1 \cdot \left(y \cdot j\right) - \color{blue}{\left(-a\right)} \cdot b\right) \]

      4. cancel-sign-sub 69.4%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(y \cdot j\right) + a \cdot b\right)} \]

      5. +-commutative 69.4%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(y \cdot j\right)\right)} \]

      6. mul-1-neg 69.4%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-y \cdot j\right)}\right) \]

      7. unsub-neg 69.4%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - y \cdot j\right)} \]

      8. *-commutative 69.4%

         \[\leadsto i \cdot \left(\color{blue}{b \cdot a} - y \cdot j\right) \]

   6. Simplified 69.4%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a - y \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.6 \cdot 10^{+79}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.25 \cdot 10^{-277}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-175}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 8: 57.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+66}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+113}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* i (* a b))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (* t (- (* c j) (* x a)))))
   (if (<= t -5.8e+66)
     t_3
     (if (<= t -3.3e-41)
       t_2
       (if (<= t -6.6e-183)
         t_1
         (if (<= t 8.8e-57)
           (+ (* x (* y z)) (* b (- (* a i) (* z c))))
           (if (<= t 3.6e+47) t_1 (if (<= t 2.05e+113) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (i * (a * b));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -5.8e+66) {
		tmp = t_3;
	} else if (t <= -3.3e-41) {
		tmp = t_2;
	} else if (t <= -6.6e-183) {
		tmp = t_1;
	} else if (t <= 8.8e-57) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (t <= 3.6e+47) {
		tmp = t_1;
	} else if (t <= 2.05e+113) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (j * ((t * c) - (y * i))) + (i * (a * b))
    t_2 = z * ((x * y) - (b * c))
    t_3 = t * ((c * j) - (x * a))
    if (t <= (-5.8d+66)) then
        tmp = t_3
    else if (t <= (-3.3d-41)) then
        tmp = t_2
    else if (t <= (-6.6d-183)) then
        tmp = t_1
    else if (t <= 8.8d-57) then
        tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
    else if (t <= 3.6d+47) then
        tmp = t_1
    else if (t <= 2.05d+113) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) + (i * (a * b));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -5.8e+66) {
		tmp = t_3;
	} else if (t <= -3.3e-41) {
		tmp = t_2;
	} else if (t <= -6.6e-183) {
		tmp = t_1;
	} else if (t <= 8.8e-57) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (t <= 3.6e+47) {
		tmp = t_1;
	} else if (t <= 2.05e+113) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (i * (a * b))
	t_2 = z * ((x * y) - (b * c))
	t_3 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -5.8e+66:
		tmp = t_3
	elif t <= -3.3e-41:
		tmp = t_2
	elif t <= -6.6e-183:
		tmp = t_1
	elif t <= 8.8e-57:
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
	elif t <= 3.6e+47:
		tmp = t_1
	elif t <= 2.05e+113:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(i * Float64(a * b)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -5.8e+66)
		tmp = t_3;
	elseif (t <= -3.3e-41)
		tmp = t_2;
	elseif (t <= -6.6e-183)
		tmp = t_1;
	elseif (t <= 8.8e-57)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (t <= 3.6e+47)
		tmp = t_1;
	elseif (t <= 2.05e+113)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) + (i * (a * b));
	t_2 = z * ((x * y) - (b * c));
	t_3 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -5.8e+66)
		tmp = t_3;
	elseif (t <= -3.3e-41)
		tmp = t_2;
	elseif (t <= -6.6e-183)
		tmp = t_1;
	elseif (t <= 8.8e-57)
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	elseif (t <= 3.6e+47)
		tmp = t_1;
	elseif (t <= 2.05e+113)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e+66], t$95$3, If[LessEqual[t, -3.3e-41], t$95$2, If[LessEqual[t, -6.6e-183], t$95$1, If[LessEqual[t, 8.8e-57], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e+47], t$95$1, If[LessEqual[t, 2.05e+113], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.79999999999999972e66 or 2.04999999999999996e113 < t

   1. Initial program 58.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 58.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 58.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 58.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 58.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 58.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 58.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 58.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 58.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 70.2%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 70.2%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 70.2%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 70.2%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 70.2%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -5.79999999999999972e66 < t < -3.30000000000000024e-41 or 3.60000000000000008e47 < t < 2.04999999999999996e113

   1. Initial program 67.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 67.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 67.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 67.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 67.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 67.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 67.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 67.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 67.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 66.5%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   if -3.30000000000000024e-41 < t < -6.5999999999999999e-183 or 8.79999999999999994e-57 < t < 3.60000000000000008e47

   1. Initial program 78.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 78.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 78.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 78.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 63.7%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. *-commutative 63.7%

         \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot a} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. associate-*r* 65.4%

         \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 65.4%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   if -6.5999999999999999e-183 < t < 8.79999999999999994e-57

   1. Initial program 80.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 80.0%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 81.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 81.6%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 81.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 81.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 81.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 81.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 72.8%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in y around inf 70.1%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b \]
   6. Step-by-step derivation

      1. *-commutative 70.1%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b \]

   7. Simplified 70.1%

      \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+66}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-41}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-183}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+47}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+113}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 9: 30.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot c\right) \cdot \left(-z\right)\\ t_2 := x \cdot \left(t \cdot \left(-a\right)\right)\\ t_3 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -5.5 \cdot 10^{+225}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{-277}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-215}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-88}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-31}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+122} \lor \neg \left(c \leq 8 \cdot 10^{+240}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* b c) (- z))) (t_2 (* x (* t (- a)))) (t_3 (* t (* c j))))
   (if (<= c -5.5e+225)
     t_3
     (if (<= c -4.5e+75)
       t_1
       (if (<= c -3.5e-277)
         t_2
         (if (<= c 4.6e-215)
           (* i (* y (- j)))
           (if (<= c 1.55e-88)
             (* y (* x z))
             (if (<= c 1.75e-31)
               (* a (* b i))
               (if (<= c 4.4e+31)
                 t_2
                 (if (or (<= c 9e+122) (not (<= c 8e+240))) t_3 t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * c) * -z;
	double t_2 = x * (t * -a);
	double t_3 = t * (c * j);
	double tmp;
	if (c <= -5.5e+225) {
		tmp = t_3;
	} else if (c <= -4.5e+75) {
		tmp = t_1;
	} else if (c <= -3.5e-277) {
		tmp = t_2;
	} else if (c <= 4.6e-215) {
		tmp = i * (y * -j);
	} else if (c <= 1.55e-88) {
		tmp = y * (x * z);
	} else if (c <= 1.75e-31) {
		tmp = a * (b * i);
	} else if (c <= 4.4e+31) {
		tmp = t_2;
	} else if ((c <= 9e+122) || !(c <= 8e+240)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (b * c) * -z
    t_2 = x * (t * -a)
    t_3 = t * (c * j)
    if (c <= (-5.5d+225)) then
        tmp = t_3
    else if (c <= (-4.5d+75)) then
        tmp = t_1
    else if (c <= (-3.5d-277)) then
        tmp = t_2
    else if (c <= 4.6d-215) then
        tmp = i * (y * -j)
    else if (c <= 1.55d-88) then
        tmp = y * (x * z)
    else if (c <= 1.75d-31) then
        tmp = a * (b * i)
    else if (c <= 4.4d+31) then
        tmp = t_2
    else if ((c <= 9d+122) .or. (.not. (c <= 8d+240))) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * c) * -z;
	double t_2 = x * (t * -a);
	double t_3 = t * (c * j);
	double tmp;
	if (c <= -5.5e+225) {
		tmp = t_3;
	} else if (c <= -4.5e+75) {
		tmp = t_1;
	} else if (c <= -3.5e-277) {
		tmp = t_2;
	} else if (c <= 4.6e-215) {
		tmp = i * (y * -j);
	} else if (c <= 1.55e-88) {
		tmp = y * (x * z);
	} else if (c <= 1.75e-31) {
		tmp = a * (b * i);
	} else if (c <= 4.4e+31) {
		tmp = t_2;
	} else if ((c <= 9e+122) || !(c <= 8e+240)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * c) * -z
	t_2 = x * (t * -a)
	t_3 = t * (c * j)
	tmp = 0
	if c <= -5.5e+225:
		tmp = t_3
	elif c <= -4.5e+75:
		tmp = t_1
	elif c <= -3.5e-277:
		tmp = t_2
	elif c <= 4.6e-215:
		tmp = i * (y * -j)
	elif c <= 1.55e-88:
		tmp = y * (x * z)
	elif c <= 1.75e-31:
		tmp = a * (b * i)
	elif c <= 4.4e+31:
		tmp = t_2
	elif (c <= 9e+122) or not (c <= 8e+240):
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * c) * Float64(-z))
	t_2 = Float64(x * Float64(t * Float64(-a)))
	t_3 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (c <= -5.5e+225)
		tmp = t_3;
	elseif (c <= -4.5e+75)
		tmp = t_1;
	elseif (c <= -3.5e-277)
		tmp = t_2;
	elseif (c <= 4.6e-215)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (c <= 1.55e-88)
		tmp = Float64(y * Float64(x * z));
	elseif (c <= 1.75e-31)
		tmp = Float64(a * Float64(b * i));
	elseif (c <= 4.4e+31)
		tmp = t_2;
	elseif ((c <= 9e+122) || !(c <= 8e+240))
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (b * c) * -z;
	t_2 = x * (t * -a);
	t_3 = t * (c * j);
	tmp = 0.0;
	if (c <= -5.5e+225)
		tmp = t_3;
	elseif (c <= -4.5e+75)
		tmp = t_1;
	elseif (c <= -3.5e-277)
		tmp = t_2;
	elseif (c <= 4.6e-215)
		tmp = i * (y * -j);
	elseif (c <= 1.55e-88)
		tmp = y * (x * z);
	elseif (c <= 1.75e-31)
		tmp = a * (b * i);
	elseif (c <= 4.4e+31)
		tmp = t_2;
	elseif ((c <= 9e+122) || ~((c <= 8e+240)))
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] * (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.5e+225], t$95$3, If[LessEqual[c, -4.5e+75], t$95$1, If[LessEqual[c, -3.5e-277], t$95$2, If[LessEqual[c, 4.6e-215], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.55e-88], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.75e-31], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.4e+31], t$95$2, If[Or[LessEqual[c, 9e+122], N[Not[LessEqual[c, 8e+240]], $MachinePrecision]], t$95$3, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -5.49999999999999985e225 or 4.4000000000000002e31 < c < 8.99999999999999995e122 or 8.00000000000000011e240 < c

   1. Initial program 55.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 55.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 55.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 55.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 55.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 55.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 55.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 55.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 55.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 51.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 51.1%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 51.1%

         \[\leadsto \left(-\color{blue}{\left(t \cdot x\right) \cdot a}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. distribute-rgt-neg-in 51.1%

         \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 51.1%

      \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in c around inf 57.4%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 52.9%

         \[\leadsto \color{blue}{\left(c \cdot t\right) \cdot j} \]

      2. *-commutative 52.9%

         \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot j \]

      3. associate-*l* 63.5%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} \]

   9. Simplified 63.5%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} \]

   if -5.49999999999999985e225 < c < -4.5000000000000004e75 or 8.99999999999999995e122 < c < 8.00000000000000011e240

   1. Initial program 60.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 60.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 60.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 60.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 60.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 60.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 60.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 60.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 60.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 60.7%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   5. Taylor expanded in t around 0 41.7%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 41.7%

         \[\leadsto \color{blue}{-c \cdot \left(z \cdot b\right)} \]

      2. *-commutative 41.7%

         \[\leadsto -c \cdot \color{blue}{\left(b \cdot z\right)} \]

      3. associate-*r* 45.2%

         \[\leadsto -\color{blue}{\left(c \cdot b\right) \cdot z} \]

      4. distribute-lft-neg-in 45.2%

         \[\leadsto \color{blue}{\left(-c \cdot b\right) \cdot z} \]

      5. *-commutative 45.2%

         \[\leadsto \left(-\color{blue}{b \cdot c}\right) \cdot z \]

   7. Simplified 45.2%

      \[\leadsto \color{blue}{\left(-b \cdot c\right) \cdot z} \]

   if -4.5000000000000004e75 < c < -3.49999999999999983e-277 or 1.74999999999999993e-31 < c < 4.4000000000000002e31

   1. Initial program 81.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 81.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 81.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 81.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in x around inf 55.6%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in y around 0 41.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot t\right)\right)} \cdot x \]
   6. Step-by-step derivation

      1. neg-mul-1 41.2%

         \[\leadsto \color{blue}{\left(-a \cdot t\right)} \cdot x \]

      2. distribute-rgt-neg-in 41.2%

         \[\leadsto \color{blue}{\left(a \cdot \left(-t\right)\right)} \cdot x \]

   7. Simplified 41.2%

      \[\leadsto \color{blue}{\left(a \cdot \left(-t\right)\right)} \cdot x \]

   if -3.49999999999999983e-277 < c < 4.5999999999999998e-215

   1. Initial program 78.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 78.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 78.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 78.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 78.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 78.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 78.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 78.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 56.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 56.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 56.5%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 56.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 56.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around 0 51.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 51.0%

         \[\leadsto \color{blue}{-y \cdot \left(i \cdot j\right)} \]

      2. associate-*r* 45.7%

         \[\leadsto -\color{blue}{\left(y \cdot i\right) \cdot j} \]

      3. *-commutative 45.7%

         \[\leadsto -\color{blue}{\left(i \cdot y\right)} \cdot j \]

      4. associate-*r* 51.0%

         \[\leadsto -\color{blue}{i \cdot \left(y \cdot j\right)} \]

      5. distribute-lft-neg-in 51.0%

         \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   9. Simplified 51.0%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   if 4.5999999999999998e-215 < c < 1.5499999999999999e-88

   1. Initial program 71.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 71.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 74.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 74.5%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 74.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 74.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 74.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 74.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 69.9%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in y around inf 43.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 1.5499999999999999e-88 < c < 1.74999999999999993e-31

   1. Initial program 87.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 87.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 87.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 87.9%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 87.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 87.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 87.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 87.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 57.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in i around inf 40.4%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 48.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.5 \cdot 10^{+225}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{+75}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{-277}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-215}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-88}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-31}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+122} \lor \neg \left(c \leq 8 \cdot 10^{+240}\right):\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \end{array} \]

Alternative 10: 50.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+157}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-66}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-132}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq -7.1 \cdot 10^{-209}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) + j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-243}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 29000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -1.35e+157)
     t_2
     (if (<= x -5.8e-66)
       (* t (- (* c j) (* x a)))
       (if (<= x -1.2e-126)
         t_1
         (if (<= x -4.6e-132)
           (* y (- (* x z) (* i j)))
           (if (<= x -7.1e-209)
             (+ (* i (* a b)) (* j (* t c)))
             (if (<= x -9.5e-243)
               (* c (- (* t j) (* z b)))
               (if (<= x 29000.0) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.35e+157) {
		tmp = t_2;
	} else if (x <= -5.8e-66) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= -1.2e-126) {
		tmp = t_1;
	} else if (x <= -4.6e-132) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= -7.1e-209) {
		tmp = (i * (a * b)) + (j * (t * c));
	} else if (x <= -9.5e-243) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 29000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-1.35d+157)) then
        tmp = t_2
    else if (x <= (-5.8d-66)) then
        tmp = t * ((c * j) - (x * a))
    else if (x <= (-1.2d-126)) then
        tmp = t_1
    else if (x <= (-4.6d-132)) then
        tmp = y * ((x * z) - (i * j))
    else if (x <= (-7.1d-209)) then
        tmp = (i * (a * b)) + (j * (t * c))
    else if (x <= (-9.5d-243)) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 29000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.35e+157) {
		tmp = t_2;
	} else if (x <= -5.8e-66) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= -1.2e-126) {
		tmp = t_1;
	} else if (x <= -4.6e-132) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= -7.1e-209) {
		tmp = (i * (a * b)) + (j * (t * c));
	} else if (x <= -9.5e-243) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 29000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.35e+157:
		tmp = t_2
	elif x <= -5.8e-66:
		tmp = t * ((c * j) - (x * a))
	elif x <= -1.2e-126:
		tmp = t_1
	elif x <= -4.6e-132:
		tmp = y * ((x * z) - (i * j))
	elif x <= -7.1e-209:
		tmp = (i * (a * b)) + (j * (t * c))
	elif x <= -9.5e-243:
		tmp = c * ((t * j) - (z * b))
	elif x <= 29000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.35e+157)
		tmp = t_2;
	elseif (x <= -5.8e-66)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (x <= -1.2e-126)
		tmp = t_1;
	elseif (x <= -4.6e-132)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (x <= -7.1e-209)
		tmp = Float64(Float64(i * Float64(a * b)) + Float64(j * Float64(t * c)));
	elseif (x <= -9.5e-243)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 29000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.35e+157)
		tmp = t_2;
	elseif (x <= -5.8e-66)
		tmp = t * ((c * j) - (x * a));
	elseif (x <= -1.2e-126)
		tmp = t_1;
	elseif (x <= -4.6e-132)
		tmp = y * ((x * z) - (i * j));
	elseif (x <= -7.1e-209)
		tmp = (i * (a * b)) + (j * (t * c));
	elseif (x <= -9.5e-243)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 29000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.35e+157], t$95$2, If[LessEqual[x, -5.8e-66], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.2e-126], t$95$1, If[LessEqual[x, -4.6e-132], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.1e-209], N[(N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.5e-243], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 29000.0], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.35e157 or 29000 < x

   1. Initial program 63.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 63.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 63.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 63.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 63.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 63.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 63.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 63.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in x around inf 63.5%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if -1.35e157 < x < -5.80000000000000023e-66

   1. Initial program 68.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 68.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 68.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 68.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 67.1%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 67.1%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 67.1%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 67.1%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 67.1%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -5.80000000000000023e-66 < x < -1.20000000000000003e-126 or -9.5000000000000005e-243 < x < 29000

   1. Initial program 80.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 80.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 80.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 80.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 66.0%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   if -1.20000000000000003e-126 < x < -4.60000000000000006e-132

   1. Initial program 61.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 61.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 61.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 61.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 61.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 61.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 61.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 61.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 61.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 60.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 60.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 60.3%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 60.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 60.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -4.60000000000000006e-132 < x < -7.1000000000000002e-209

   1. Initial program 65.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 65.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 65.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 65.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 65.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 65.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 65.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 65.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 65.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 70.7%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. *-commutative 70.7%

         \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot a} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. associate-*r* 70.8%

         \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 70.8%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in t around inf 71.0%

      \[\leadsto i \cdot \left(b \cdot a\right) + j \cdot \color{blue}{\left(c \cdot t\right)} \]

   if -7.1000000000000002e-209 < x < -9.5000000000000005e-243

   1. Initial program 50.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 50.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 50.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 50.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 50.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 50.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 50.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 50.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 50.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 65.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-66}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-126}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-132}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq -7.1 \cdot 10^{-209}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) + j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-243}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 29000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 11: 48.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-204}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-103} \lor \neg \left(a \leq 7 \cdot 10^{+58}\right) \land a \leq 5.8 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -1.25e+86)
     t_2
     (if (<= a -7e-141)
       t_1
       (if (<= a -2.4e-204)
         (* y (* x z))
         (if (or (<= a 8e-103) (and (not (<= a 7e+58)) (<= a 5.8e+144)))
           t_1
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.25e+86) {
		tmp = t_2;
	} else if (a <= -7e-141) {
		tmp = t_1;
	} else if (a <= -2.4e-204) {
		tmp = y * (x * z);
	} else if ((a <= 8e-103) || (!(a <= 7e+58) && (a <= 5.8e+144))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-1.25d+86)) then
        tmp = t_2
    else if (a <= (-7d-141)) then
        tmp = t_1
    else if (a <= (-2.4d-204)) then
        tmp = y * (x * z)
    else if ((a <= 8d-103) .or. (.not. (a <= 7d+58)) .and. (a <= 5.8d+144)) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1.25e+86) {
		tmp = t_2;
	} else if (a <= -7e-141) {
		tmp = t_1;
	} else if (a <= -2.4e-204) {
		tmp = y * (x * z);
	} else if ((a <= 8e-103) || (!(a <= 7e+58) && (a <= 5.8e+144))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -1.25e+86:
		tmp = t_2
	elif a <= -7e-141:
		tmp = t_1
	elif a <= -2.4e-204:
		tmp = y * (x * z)
	elif (a <= 8e-103) or (not (a <= 7e+58) and (a <= 5.8e+144)):
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.25e+86)
		tmp = t_2;
	elseif (a <= -7e-141)
		tmp = t_1;
	elseif (a <= -2.4e-204)
		tmp = Float64(y * Float64(x * z));
	elseif ((a <= 8e-103) || (!(a <= 7e+58) && (a <= 5.8e+144)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -1.25e+86)
		tmp = t_2;
	elseif (a <= -7e-141)
		tmp = t_1;
	elseif (a <= -2.4e-204)
		tmp = y * (x * z);
	elseif ((a <= 8e-103) || (~((a <= 7e+58)) && (a <= 5.8e+144)))
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.25e+86], t$95$2, If[LessEqual[a, -7e-141], t$95$1, If[LessEqual[a, -2.4e-204], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 8e-103], And[N[Not[LessEqual[a, 7e+58]], $MachinePrecision], LessEqual[a, 5.8e+144]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.2499999999999999e86 or 7.99999999999999966e-103 < a < 6.9999999999999995e58 or 5.79999999999999996e144 < a

   1. Initial program 66.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 66.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 66.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 66.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 66.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 66.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 66.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 66.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 66.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 66.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 66.4%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 66.4%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 66.4%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 66.4%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 66.4%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 66.4%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 66.4%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   if -1.2499999999999999e86 < a < -7.0000000000000006e-141 or -2.4e-204 < a < 7.99999999999999966e-103 or 6.9999999999999995e58 < a < 5.79999999999999996e144

   1. Initial program 75.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 75.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 75.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 75.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 75.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 75.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 75.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 75.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 55.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if -7.0000000000000006e-141 < a < -2.4e-204

   1. Initial program 33.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 33.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 56.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 56.2%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 56.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 56.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 56.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 56.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 67.3%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in y around inf 89.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{+86}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-141}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-204}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-103} \lor \neg \left(a \leq 7 \cdot 10^{+58}\right) \land a \leq 5.8 \cdot 10^{+144}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 12: 29.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(-x \cdot t\right)\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+85}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-115}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-263}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 58000000:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+187}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* x t)))))
   (if (<= z -8.8e+85)
     (* (* b c) (- z))
     (if (<= z -2.5e-37)
       t_1
       (if (<= z -7.8e-115)
         (* j (* t c))
         (if (<= z -8.8e-223)
           t_1
           (if (<= z 5.6e-263)
             (* i (* y (- j)))
             (if (<= z 58000000.0)
               (* c (* t j))
               (if (<= z 1.8e+187) (* x (* y z)) (* c (- (* z b))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * -(x * t);
	double tmp;
	if (z <= -8.8e+85) {
		tmp = (b * c) * -z;
	} else if (z <= -2.5e-37) {
		tmp = t_1;
	} else if (z <= -7.8e-115) {
		tmp = j * (t * c);
	} else if (z <= -8.8e-223) {
		tmp = t_1;
	} else if (z <= 5.6e-263) {
		tmp = i * (y * -j);
	} else if (z <= 58000000.0) {
		tmp = c * (t * j);
	} else if (z <= 1.8e+187) {
		tmp = x * (y * z);
	} else {
		tmp = c * -(z * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * -(x * t)
    if (z <= (-8.8d+85)) then
        tmp = (b * c) * -z
    else if (z <= (-2.5d-37)) then
        tmp = t_1
    else if (z <= (-7.8d-115)) then
        tmp = j * (t * c)
    else if (z <= (-8.8d-223)) then
        tmp = t_1
    else if (z <= 5.6d-263) then
        tmp = i * (y * -j)
    else if (z <= 58000000.0d0) then
        tmp = c * (t * j)
    else if (z <= 1.8d+187) then
        tmp = x * (y * z)
    else
        tmp = c * -(z * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * -(x * t);
	double tmp;
	if (z <= -8.8e+85) {
		tmp = (b * c) * -z;
	} else if (z <= -2.5e-37) {
		tmp = t_1;
	} else if (z <= -7.8e-115) {
		tmp = j * (t * c);
	} else if (z <= -8.8e-223) {
		tmp = t_1;
	} else if (z <= 5.6e-263) {
		tmp = i * (y * -j);
	} else if (z <= 58000000.0) {
		tmp = c * (t * j);
	} else if (z <= 1.8e+187) {
		tmp = x * (y * z);
	} else {
		tmp = c * -(z * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * -(x * t)
	tmp = 0
	if z <= -8.8e+85:
		tmp = (b * c) * -z
	elif z <= -2.5e-37:
		tmp = t_1
	elif z <= -7.8e-115:
		tmp = j * (t * c)
	elif z <= -8.8e-223:
		tmp = t_1
	elif z <= 5.6e-263:
		tmp = i * (y * -j)
	elif z <= 58000000.0:
		tmp = c * (t * j)
	elif z <= 1.8e+187:
		tmp = x * (y * z)
	else:
		tmp = c * -(z * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(-Float64(x * t)))
	tmp = 0.0
	if (z <= -8.8e+85)
		tmp = Float64(Float64(b * c) * Float64(-z));
	elseif (z <= -2.5e-37)
		tmp = t_1;
	elseif (z <= -7.8e-115)
		tmp = Float64(j * Float64(t * c));
	elseif (z <= -8.8e-223)
		tmp = t_1;
	elseif (z <= 5.6e-263)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (z <= 58000000.0)
		tmp = Float64(c * Float64(t * j));
	elseif (z <= 1.8e+187)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(c * Float64(-Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * -(x * t);
	tmp = 0.0;
	if (z <= -8.8e+85)
		tmp = (b * c) * -z;
	elseif (z <= -2.5e-37)
		tmp = t_1;
	elseif (z <= -7.8e-115)
		tmp = j * (t * c);
	elseif (z <= -8.8e-223)
		tmp = t_1;
	elseif (z <= 5.6e-263)
		tmp = i * (y * -j);
	elseif (z <= 58000000.0)
		tmp = c * (t * j);
	elseif (z <= 1.8e+187)
		tmp = x * (y * z);
	else
		tmp = c * -(z * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * (-N[(x * t), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[z, -8.8e+85], N[(N[(b * c), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[z, -2.5e-37], t$95$1, If[LessEqual[z, -7.8e-115], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.8e-223], t$95$1, If[LessEqual[z, 5.6e-263], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 58000000.0], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+187], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(c * (-N[(z * b), $MachinePrecision])), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -8.8000000000000007e85

   1. Initial program 58.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 58.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 58.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 58.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 58.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 58.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 58.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 58.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 58.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 50.8%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   5. Taylor expanded in t around 0 48.2%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 48.2%

         \[\leadsto \color{blue}{-c \cdot \left(z \cdot b\right)} \]

      2. *-commutative 48.2%

         \[\leadsto -c \cdot \color{blue}{\left(b \cdot z\right)} \]

      3. associate-*r* 48.3%

         \[\leadsto -\color{blue}{\left(c \cdot b\right) \cdot z} \]

      4. distribute-lft-neg-in 48.3%

         \[\leadsto \color{blue}{\left(-c \cdot b\right) \cdot z} \]

      5. *-commutative 48.3%

         \[\leadsto \left(-\color{blue}{b \cdot c}\right) \cdot z \]

   7. Simplified 48.3%

      \[\leadsto \color{blue}{\left(-b \cdot c\right) \cdot z} \]

   if -8.8000000000000007e85 < z < -2.4999999999999999e-37 or -7.7999999999999997e-115 < z < -8.80000000000000036e-223

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 73.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 73.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 73.9%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 73.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 73.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 73.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 73.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 70.2%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in t around inf 47.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 47.8%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot a\right)} \]

      2. neg-mul-1 47.8%

         \[\leadsto \color{blue}{-\left(t \cdot x\right) \cdot a} \]

      3. distribute-rgt-neg-in 47.8%

         \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} \]

   7. Simplified 47.8%

      \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} \]

   if -2.4999999999999999e-37 < z < -7.7999999999999997e-115

   1. Initial program 87.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 87.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 87.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 87.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 87.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 87.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 87.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 87.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 87.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 52.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 52.2%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 52.2%

         \[\leadsto \left(-\color{blue}{\left(t \cdot x\right) \cdot a}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. distribute-rgt-neg-in 52.2%

         \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 52.2%

      \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in c around inf 38.6%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 44.4%

         \[\leadsto \color{blue}{\left(c \cdot t\right) \cdot j} \]

      2. *-commutative 44.4%

         \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot j \]

   9. Simplified 44.4%

      \[\leadsto \color{blue}{\left(t \cdot c\right) \cdot j} \]

   if -8.80000000000000036e-223 < z < 5.6000000000000001e-263

   1. Initial program 76.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 76.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 76.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 76.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 76.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 76.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 76.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 76.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 76.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 41.4%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 41.4%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 41.4%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 41.4%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 41.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around 0 41.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 41.5%

         \[\leadsto \color{blue}{-y \cdot \left(i \cdot j\right)} \]

      2. associate-*r* 38.6%

         \[\leadsto -\color{blue}{\left(y \cdot i\right) \cdot j} \]

      3. *-commutative 38.6%

         \[\leadsto -\color{blue}{\left(i \cdot y\right)} \cdot j \]

      4. associate-*r* 46.9%

         \[\leadsto -\color{blue}{i \cdot \left(y \cdot j\right)} \]

      5. distribute-lft-neg-in 46.9%

         \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   9. Simplified 46.9%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   if 5.6000000000000001e-263 < z < 5.8e7

   1. Initial program 70.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 70.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 70.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 70.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 70.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 70.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 70.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 70.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 70.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 47.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 47.3%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 47.3%

         \[\leadsto \left(-\color{blue}{\left(t \cdot x\right) \cdot a}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. distribute-rgt-neg-in 47.3%

         \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 47.3%

      \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in c around inf 39.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if 5.8e7 < z < 1.80000000000000018e187

   1. Initial program 68.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 68.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 74.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 74.0%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 74.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 74.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 74.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 74.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 58.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in y around inf 38.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 40.7%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. *-commutative 40.7%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

   7. Simplified 40.7%

      \[\leadsto \color{blue}{\left(z \cdot y\right) \cdot x} \]

   if 1.80000000000000018e187 < z

   1. Initial program 55.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 55.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 60.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 60.4%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 60.4%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 60.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 60.4%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 60.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 60.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in c around inf 58.7%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. *-commutative 58.7%

         \[\leadsto -1 \cdot \left(c \cdot \color{blue}{\left(b \cdot z\right)}\right) \]

      2. mul-1-neg 58.7%

         \[\leadsto \color{blue}{-c \cdot \left(b \cdot z\right)} \]

      3. distribute-rgt-neg-in 58.7%

         \[\leadsto \color{blue}{c \cdot \left(-b \cdot z\right)} \]

      4. *-commutative 58.7%

         \[\leadsto c \cdot \left(-\color{blue}{z \cdot b}\right) \]

   7. Simplified 58.7%

      \[\leadsto \color{blue}{c \cdot \left(-z \cdot b\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+85}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-37}:\\ \;\;\;\;a \cdot \left(-x \cdot t\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-115}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-223}:\\ \;\;\;\;a \cdot \left(-x \cdot t\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-263}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;z \leq 58000000:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+187}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(-z \cdot b\right)\\ \end{array} \]

Alternative 13: 51.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-243}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-138}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -4.8e+65)
     t_2
     (if (<= y -1.5e-92)
       t_1
       (if (<= y 1.5e-243)
         (* a (- (* b i) (* x t)))
         (if (<= y 1.65e-138)
           (* t (- (* c j) (* x a)))
           (if (<= y 6e+98) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -4.8e+65) {
		tmp = t_2;
	} else if (y <= -1.5e-92) {
		tmp = t_1;
	} else if (y <= 1.5e-243) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 1.65e-138) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 6e+98) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-4.8d+65)) then
        tmp = t_2
    else if (y <= (-1.5d-92)) then
        tmp = t_1
    else if (y <= 1.5d-243) then
        tmp = a * ((b * i) - (x * t))
    else if (y <= 1.65d-138) then
        tmp = t * ((c * j) - (x * a))
    else if (y <= 6d+98) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -4.8e+65) {
		tmp = t_2;
	} else if (y <= -1.5e-92) {
		tmp = t_1;
	} else if (y <= 1.5e-243) {
		tmp = a * ((b * i) - (x * t));
	} else if (y <= 1.65e-138) {
		tmp = t * ((c * j) - (x * a));
	} else if (y <= 6e+98) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -4.8e+65:
		tmp = t_2
	elif y <= -1.5e-92:
		tmp = t_1
	elif y <= 1.5e-243:
		tmp = a * ((b * i) - (x * t))
	elif y <= 1.65e-138:
		tmp = t * ((c * j) - (x * a))
	elif y <= 6e+98:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -4.8e+65)
		tmp = t_2;
	elseif (y <= -1.5e-92)
		tmp = t_1;
	elseif (y <= 1.5e-243)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (y <= 1.65e-138)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (y <= 6e+98)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -4.8e+65)
		tmp = t_2;
	elseif (y <= -1.5e-92)
		tmp = t_1;
	elseif (y <= 1.5e-243)
		tmp = a * ((b * i) - (x * t));
	elseif (y <= 1.65e-138)
		tmp = t * ((c * j) - (x * a));
	elseif (y <= 6e+98)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+65], t$95$2, If[LessEqual[y, -1.5e-92], t$95$1, If[LessEqual[y, 1.5e-243], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-138], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+98], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.8000000000000003e65 or 6.0000000000000003e98 < y

   1. Initial program 55.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 55.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 55.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 55.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 55.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 55.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 55.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 55.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 55.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 62.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 62.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 62.5%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 62.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 62.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -4.8000000000000003e65 < y < -1.50000000000000007e-92 or 1.64999999999999991e-138 < y < 6.0000000000000003e98

   1. Initial program 76.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 76.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 76.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 76.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 76.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 58.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if -1.50000000000000007e-92 < y < 1.5000000000000001e-243

   1. Initial program 82.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 82.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 82.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 82.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 82.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 82.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 82.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 82.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 82.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 58.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 58.1%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 58.1%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 58.1%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 58.1%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 58.1%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 58.1%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 58.1%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   if 1.5000000000000001e-243 < y < 1.64999999999999991e-138

   1. Initial program 69.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 69.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 69.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 69.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 69.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 69.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 69.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 69.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 69.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 70.6%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 70.6%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 70.6%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 70.6%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 70.6%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-92}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-243}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-138}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+98}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 14: 47.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{+91}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -5.9 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-205}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= a -4.2e+91)
     (* a (- (* b i) (* x t)))
     (if (<= a -5.9e-142)
       t_1
       (if (<= a -4.5e-205)
         (* y (* x z))
         (if (<= a 5.9e-36) t_1 (* t (- (* c j) (* x a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (a <= -4.2e+91) {
		tmp = a * ((b * i) - (x * t));
	} else if (a <= -5.9e-142) {
		tmp = t_1;
	} else if (a <= -4.5e-205) {
		tmp = y * (x * z);
	} else if (a <= 5.9e-36) {
		tmp = t_1;
	} else {
		tmp = t * ((c * j) - (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    if (a <= (-4.2d+91)) then
        tmp = a * ((b * i) - (x * t))
    else if (a <= (-5.9d-142)) then
        tmp = t_1
    else if (a <= (-4.5d-205)) then
        tmp = y * (x * z)
    else if (a <= 5.9d-36) then
        tmp = t_1
    else
        tmp = t * ((c * j) - (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (a <= -4.2e+91) {
		tmp = a * ((b * i) - (x * t));
	} else if (a <= -5.9e-142) {
		tmp = t_1;
	} else if (a <= -4.5e-205) {
		tmp = y * (x * z);
	} else if (a <= 5.9e-36) {
		tmp = t_1;
	} else {
		tmp = t * ((c * j) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if a <= -4.2e+91:
		tmp = a * ((b * i) - (x * t))
	elif a <= -5.9e-142:
		tmp = t_1
	elif a <= -4.5e-205:
		tmp = y * (x * z)
	elif a <= 5.9e-36:
		tmp = t_1
	else:
		tmp = t * ((c * j) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (a <= -4.2e+91)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (a <= -5.9e-142)
		tmp = t_1;
	elseif (a <= -4.5e-205)
		tmp = Float64(y * Float64(x * z));
	elseif (a <= 5.9e-36)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (a <= -4.2e+91)
		tmp = a * ((b * i) - (x * t));
	elseif (a <= -5.9e-142)
		tmp = t_1;
	elseif (a <= -4.5e-205)
		tmp = y * (x * z);
	elseif (a <= 5.9e-36)
		tmp = t_1;
	else
		tmp = t * ((c * j) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.2e+91], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.9e-142], t$95$1, If[LessEqual[a, -4.5e-205], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.9e-36], t$95$1, N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.20000000000000015e91

   1. Initial program 63.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 63.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 63.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 63.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 63.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 63.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 63.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 63.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 77.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 77.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 77.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 77.8%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 77.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 77.8%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 77.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 77.8%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   if -4.20000000000000015e91 < a < -5.89999999999999966e-142 or -4.49999999999999956e-205 < a < 5.89999999999999995e-36

   1. Initial program 78.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 78.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 78.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 78.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 54.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if -5.89999999999999966e-142 < a < -4.49999999999999956e-205

   1. Initial program 33.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 33.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 56.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 56.2%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 56.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 56.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 56.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 56.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 67.3%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in y around inf 89.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 5.89999999999999995e-36 < a

   1. Initial program 64.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 64.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 64.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 64.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 64.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 64.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 64.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 64.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 64.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 51.4%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 51.4%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 51.4%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 51.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 51.4%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{+91}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -5.9 \cdot 10^{-142}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-205}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;a \leq 5.9 \cdot 10^{-36}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 15: 44.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+188}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-84}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-242}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+32}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -9e+188)
   (* z (- (* x y) (* b c)))
   (if (<= x -4e-84)
     (* t (- (* c j) (* x a)))
     (if (<= x -6.6e-242)
       (* c (- (* t j) (* z b)))
       (if (<= x 1.1e+32)
         (* b (- (* a i) (* z c)))
         (* y (- (* x z) (* i j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -9e+188) {
		tmp = z * ((x * y) - (b * c));
	} else if (x <= -4e-84) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= -6.6e-242) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 1.1e+32) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= (-9d+188)) then
        tmp = z * ((x * y) - (b * c))
    else if (x <= (-4d-84)) then
        tmp = t * ((c * j) - (x * a))
    else if (x <= (-6.6d-242)) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 1.1d+32) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = y * ((x * z) - (i * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -9e+188) {
		tmp = z * ((x * y) - (b * c));
	} else if (x <= -4e-84) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= -6.6e-242) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 1.1e+32) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -9e+188:
		tmp = z * ((x * y) - (b * c))
	elif x <= -4e-84:
		tmp = t * ((c * j) - (x * a))
	elif x <= -6.6e-242:
		tmp = c * ((t * j) - (z * b))
	elif x <= 1.1e+32:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = y * ((x * z) - (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -9e+188)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (x <= -4e-84)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (x <= -6.6e-242)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 1.1e+32)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -9e+188)
		tmp = z * ((x * y) - (b * c));
	elseif (x <= -4e-84)
		tmp = t * ((c * j) - (x * a));
	elseif (x <= -6.6e-242)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 1.1e+32)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = y * ((x * z) - (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -9e+188], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4e-84], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.6e-242], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e+32], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -9.00000000000000021e188

   1. Initial program 39.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 39.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 39.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 39.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 39.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 39.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 39.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 39.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 39.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 68.3%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   if -9.00000000000000021e188 < x < -4.0000000000000001e-84

   1. Initial program 70.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 70.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 70.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 70.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 70.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 70.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 70.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 70.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 70.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 61.1%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 61.1%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 61.1%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 61.1%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 61.1%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -4.0000000000000001e-84 < x < -6.59999999999999963e-242

   1. Initial program 64.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 64.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 64.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 64.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 64.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 64.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 64.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 64.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 64.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 59.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if -6.59999999999999963e-242 < x < 1.1e32

   1. Initial program 78.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 78.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 78.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 78.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 78.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 78.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 78.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 78.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 63.1%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   if 1.1e32 < x

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 74.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 74.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 74.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 74.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 74.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 74.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 74.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 74.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 51.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 51.1%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 51.1%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 51.1%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 51.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+188}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-84}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-242}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+32}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 16: 50.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{+155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-85}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-243}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 28000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -3.1e+155)
     t_1
     (if (<= x -3.7e-85)
       (* t (- (* c j) (* x a)))
       (if (<= x -2.7e-243)
         (* c (- (* t j) (* z b)))
         (if (<= x 28000.0) (* b (- (* a i) (* z c))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -3.1e+155) {
		tmp = t_1;
	} else if (x <= -3.7e-85) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= -2.7e-243) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 28000.0) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-3.1d+155)) then
        tmp = t_1
    else if (x <= (-3.7d-85)) then
        tmp = t * ((c * j) - (x * a))
    else if (x <= (-2.7d-243)) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 28000.0d0) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -3.1e+155) {
		tmp = t_1;
	} else if (x <= -3.7e-85) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= -2.7e-243) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 28000.0) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -3.1e+155:
		tmp = t_1
	elif x <= -3.7e-85:
		tmp = t * ((c * j) - (x * a))
	elif x <= -2.7e-243:
		tmp = c * ((t * j) - (z * b))
	elif x <= 28000.0:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -3.1e+155)
		tmp = t_1;
	elseif (x <= -3.7e-85)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (x <= -2.7e-243)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 28000.0)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -3.1e+155)
		tmp = t_1;
	elseif (x <= -3.7e-85)
		tmp = t * ((c * j) - (x * a));
	elseif (x <= -2.7e-243)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 28000.0)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.1e+155], t$95$1, If[LessEqual[x, -3.7e-85], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.7e-243], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 28000.0], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.09999999999999989e155 or 28000 < x

   1. Initial program 63.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 63.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 63.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 63.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 63.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 63.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 63.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 63.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 63.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in x around inf 63.5%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if -3.09999999999999989e155 < x < -3.69999999999999983e-85

   1. Initial program 70.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 70.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 70.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 70.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 70.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 70.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 70.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 70.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 70.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 64.6%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 64.6%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 64.6%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 64.6%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 64.6%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -3.69999999999999983e-85 < x < -2.7000000000000001e-243

   1. Initial program 64.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 64.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 64.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 64.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 64.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 64.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 64.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 64.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 64.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 59.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if -2.7000000000000001e-243 < x < 28000

   1. Initial program 79.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 79.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 79.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 79.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 79.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 79.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 79.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 79.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 65.9%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-85}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-243}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 28000:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 17: 41.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b \cdot c\right) \cdot \left(-z\right)\\ t_2 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -3.4 \cdot 10^{+224}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 10^{+71}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+122} \lor \neg \left(c \leq 4.5 \cdot 10^{+240}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* b c) (- z))) (t_2 (* t (* c j))))
   (if (<= c -3.4e+224)
     t_2
     (if (<= c -3.4e+74)
       t_1
       (if (<= c 1e+71)
         (* a (- (* b i) (* x t)))
         (if (or (<= c 9.2e+122) (not (<= c 4.5e+240))) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * c) * -z;
	double t_2 = t * (c * j);
	double tmp;
	if (c <= -3.4e+224) {
		tmp = t_2;
	} else if (c <= -3.4e+74) {
		tmp = t_1;
	} else if (c <= 1e+71) {
		tmp = a * ((b * i) - (x * t));
	} else if ((c <= 9.2e+122) || !(c <= 4.5e+240)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * c) * -z
    t_2 = t * (c * j)
    if (c <= (-3.4d+224)) then
        tmp = t_2
    else if (c <= (-3.4d+74)) then
        tmp = t_1
    else if (c <= 1d+71) then
        tmp = a * ((b * i) - (x * t))
    else if ((c <= 9.2d+122) .or. (.not. (c <= 4.5d+240))) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * c) * -z;
	double t_2 = t * (c * j);
	double tmp;
	if (c <= -3.4e+224) {
		tmp = t_2;
	} else if (c <= -3.4e+74) {
		tmp = t_1;
	} else if (c <= 1e+71) {
		tmp = a * ((b * i) - (x * t));
	} else if ((c <= 9.2e+122) || !(c <= 4.5e+240)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * c) * -z
	t_2 = t * (c * j)
	tmp = 0
	if c <= -3.4e+224:
		tmp = t_2
	elif c <= -3.4e+74:
		tmp = t_1
	elif c <= 1e+71:
		tmp = a * ((b * i) - (x * t))
	elif (c <= 9.2e+122) or not (c <= 4.5e+240):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * c) * Float64(-z))
	t_2 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (c <= -3.4e+224)
		tmp = t_2;
	elseif (c <= -3.4e+74)
		tmp = t_1;
	elseif (c <= 1e+71)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif ((c <= 9.2e+122) || !(c <= 4.5e+240))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (b * c) * -z;
	t_2 = t * (c * j);
	tmp = 0.0;
	if (c <= -3.4e+224)
		tmp = t_2;
	elseif (c <= -3.4e+74)
		tmp = t_1;
	elseif (c <= 1e+71)
		tmp = a * ((b * i) - (x * t));
	elseif ((c <= 9.2e+122) || ~((c <= 4.5e+240)))
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] * (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.4e+224], t$95$2, If[LessEqual[c, -3.4e+74], t$95$1, If[LessEqual[c, 1e+71], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 9.2e+122], N[Not[LessEqual[c, 4.5e+240]], $MachinePrecision]], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.4000000000000002e224 or 1e71 < c < 9.2000000000000002e122 or 4.49999999999999979e240 < c

   1. Initial program 58.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 58.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 58.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 58.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 58.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 58.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 58.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 58.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 58.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 51.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 51.9%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 51.9%

         \[\leadsto \left(-\color{blue}{\left(t \cdot x\right) \cdot a}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. distribute-rgt-neg-in 51.9%

         \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 51.9%

      \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in c around inf 60.7%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 55.6%

         \[\leadsto \color{blue}{\left(c \cdot t\right) \cdot j} \]

      2. *-commutative 55.6%

         \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot j \]

      3. associate-*l* 67.6%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} \]

   9. Simplified 67.6%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} \]

   if -3.4000000000000002e224 < c < -3.3999999999999999e74 or 9.2000000000000002e122 < c < 4.49999999999999979e240

   1. Initial program 60.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 60.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 60.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 60.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 60.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 60.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 60.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 60.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 60.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 60.7%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   5. Taylor expanded in t around 0 41.7%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 41.7%

         \[\leadsto \color{blue}{-c \cdot \left(z \cdot b\right)} \]

      2. *-commutative 41.7%

         \[\leadsto -c \cdot \color{blue}{\left(b \cdot z\right)} \]

      3. associate-*r* 45.2%

         \[\leadsto -\color{blue}{\left(c \cdot b\right) \cdot z} \]

      4. distribute-lft-neg-in 45.2%

         \[\leadsto \color{blue}{\left(-c \cdot b\right) \cdot z} \]

      5. *-commutative 45.2%

         \[\leadsto \left(-\color{blue}{b \cdot c}\right) \cdot z \]

   7. Simplified 45.2%

      \[\leadsto \color{blue}{\left(-b \cdot c\right) \cdot z} \]

   if -3.3999999999999999e74 < c < 1e71

   1. Initial program 77.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 77.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 77.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 77.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 77.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 77.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 77.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 77.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 77.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 53.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 53.5%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 53.5%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 53.5%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 53.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 53.5%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 53.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 53.5%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.4 \cdot 10^{+224}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{+74}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \mathbf{elif}\;c \leq 10^{+71}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+122} \lor \neg \left(c \leq 4.5 \cdot 10^{+240}\right):\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c\right) \cdot \left(-z\right)\\ \end{array} \]

Alternative 18: 30.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;t \leq -1.48 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.04 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+46}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+133}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 10^{+172}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= t -1.48e+47)
     t_1
     (if (<= t -1.04e-48)
       (* y (* x z))
       (if (<= t 2.1e+46)
         (* a (* b i))
         (if (<= t 2.15e+133)
           (* i (* y (- j)))
           (if (<= t 1e+172) (* j (* t c)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (t <= -1.48e+47) {
		tmp = t_1;
	} else if (t <= -1.04e-48) {
		tmp = y * (x * z);
	} else if (t <= 2.1e+46) {
		tmp = a * (b * i);
	} else if (t <= 2.15e+133) {
		tmp = i * (y * -j);
	} else if (t <= 1e+172) {
		tmp = j * (t * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * j)
    if (t <= (-1.48d+47)) then
        tmp = t_1
    else if (t <= (-1.04d-48)) then
        tmp = y * (x * z)
    else if (t <= 2.1d+46) then
        tmp = a * (b * i)
    else if (t <= 2.15d+133) then
        tmp = i * (y * -j)
    else if (t <= 1d+172) then
        tmp = j * (t * c)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (t <= -1.48e+47) {
		tmp = t_1;
	} else if (t <= -1.04e-48) {
		tmp = y * (x * z);
	} else if (t <= 2.1e+46) {
		tmp = a * (b * i);
	} else if (t <= 2.15e+133) {
		tmp = i * (y * -j);
	} else if (t <= 1e+172) {
		tmp = j * (t * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if t <= -1.48e+47:
		tmp = t_1
	elif t <= -1.04e-48:
		tmp = y * (x * z)
	elif t <= 2.1e+46:
		tmp = a * (b * i)
	elif t <= 2.15e+133:
		tmp = i * (y * -j)
	elif t <= 1e+172:
		tmp = j * (t * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (t <= -1.48e+47)
		tmp = t_1;
	elseif (t <= -1.04e-48)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 2.1e+46)
		tmp = Float64(a * Float64(b * i));
	elseif (t <= 2.15e+133)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (t <= 1e+172)
		tmp = Float64(j * Float64(t * c));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	tmp = 0.0;
	if (t <= -1.48e+47)
		tmp = t_1;
	elseif (t <= -1.04e-48)
		tmp = y * (x * z);
	elseif (t <= 2.1e+46)
		tmp = a * (b * i);
	elseif (t <= 2.15e+133)
		tmp = i * (y * -j);
	elseif (t <= 1e+172)
		tmp = j * (t * c);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.48e+47], t$95$1, If[LessEqual[t, -1.04e-48], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e+46], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.15e+133], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+172], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.47999999999999996e47 or 1.0000000000000001e172 < t

   1. Initial program 54.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 54.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 54.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 54.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 54.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 54.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 54.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 54.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 54.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 47.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 47.2%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 47.2%

         \[\leadsto \left(-\color{blue}{\left(t \cdot x\right) \cdot a}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. distribute-rgt-neg-in 47.2%

         \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 47.2%

      \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in c around inf 48.2%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -1.47999999999999996e47 < t < -1.03999999999999998e-48

   1. Initial program 69.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 69.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 69.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 69.8%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 69.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 69.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 69.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 69.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 44.3%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in y around inf 32.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -1.03999999999999998e-48 < t < 2.1e46

   1. Initial program 79.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 79.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 80.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 80.7%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 80.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 80.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 80.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 80.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 64.9%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in i around inf 37.1%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   if 2.1e46 < t < 2.14999999999999997e133

   1. Initial program 59.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 59.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 59.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 59.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 59.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 59.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 59.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 59.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 59.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 54.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 54.1%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 54.1%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 54.1%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 54.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around 0 42.2%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 42.2%

         \[\leadsto \color{blue}{-y \cdot \left(i \cdot j\right)} \]

      2. associate-*r* 31.1%

         \[\leadsto -\color{blue}{\left(y \cdot i\right) \cdot j} \]

      3. *-commutative 31.1%

         \[\leadsto -\color{blue}{\left(i \cdot y\right)} \cdot j \]

      4. associate-*r* 42.3%

         \[\leadsto -\color{blue}{i \cdot \left(y \cdot j\right)} \]

      5. distribute-lft-neg-in 42.3%

         \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   9. Simplified 42.3%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   if 2.14999999999999997e133 < t < 1.0000000000000001e172

   1. Initial program 92.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 92.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 92.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 92.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 92.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 92.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 92.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 92.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 69.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 69.6%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 69.6%

         \[\leadsto \left(-\color{blue}{\left(t \cdot x\right) \cdot a}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. distribute-rgt-neg-in 69.6%

         \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 69.6%

      \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in c around inf 40.6%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 55.1%

         \[\leadsto \color{blue}{\left(c \cdot t\right) \cdot j} \]

      2. *-commutative 55.1%

         \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot j \]

   9. Simplified 55.1%

      \[\leadsto \color{blue}{\left(t \cdot c\right) \cdot j} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.48 \cdot 10^{+47}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -1.04 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+46}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+133}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 10^{+172}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 19: 43.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{-90}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-242}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+35}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -7.4e-90)
   (* t (- (* c j) (* x a)))
   (if (<= x -3.8e-242)
     (* c (- (* t j) (* z b)))
     (if (<= x 1.95e+35)
       (* b (- (* a i) (* z c)))
       (* y (- (* x z) (* i j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -7.4e-90) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= -3.8e-242) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 1.95e+35) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= (-7.4d-90)) then
        tmp = t * ((c * j) - (x * a))
    else if (x <= (-3.8d-242)) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 1.95d+35) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = y * ((x * z) - (i * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -7.4e-90) {
		tmp = t * ((c * j) - (x * a));
	} else if (x <= -3.8e-242) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 1.95e+35) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -7.4e-90:
		tmp = t * ((c * j) - (x * a))
	elif x <= -3.8e-242:
		tmp = c * ((t * j) - (z * b))
	elif x <= 1.95e+35:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = y * ((x * z) - (i * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -7.4e-90)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (x <= -3.8e-242)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 1.95e+35)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -7.4e-90)
		tmp = t * ((c * j) - (x * a));
	elseif (x <= -3.8e-242)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 1.95e+35)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = y * ((x * z) - (i * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -7.4e-90], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.8e-242], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.95e+35], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.40000000000000035e-90

   1. Initial program 58.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 58.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 58.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 58.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 58.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 58.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 58.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 58.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 58.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 55.9%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 55.9%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 55.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 55.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 55.9%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -7.40000000000000035e-90 < x < -3.8000000000000002e-242

   1. Initial program 64.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 64.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 64.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 64.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 64.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 64.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 64.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 64.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 64.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 59.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if -3.8000000000000002e-242 < x < 1.95e35

   1. Initial program 78.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 78.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 78.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 78.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 78.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 78.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 78.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 78.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 63.1%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   if 1.95e35 < x

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 74.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 74.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 74.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 74.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 74.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 74.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 74.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 74.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in y around inf 51.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]
   5. Step-by-step derivation

      1. +-commutative 51.1%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 51.1%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 51.1%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 51.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{-90}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-242}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+35}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 20: 30.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= t -1.9e+48)
     t_1
     (if (<= t -1.05e-48)
       (* y (* x z))
       (if (<= t 2.65e+45) (* a (* b i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (t <= -1.9e+48) {
		tmp = t_1;
	} else if (t <= -1.05e-48) {
		tmp = y * (x * z);
	} else if (t <= 2.65e+45) {
		tmp = a * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * j)
    if (t <= (-1.9d+48)) then
        tmp = t_1
    else if (t <= (-1.05d-48)) then
        tmp = y * (x * z)
    else if (t <= 2.65d+45) then
        tmp = a * (b * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (t <= -1.9e+48) {
		tmp = t_1;
	} else if (t <= -1.05e-48) {
		tmp = y * (x * z);
	} else if (t <= 2.65e+45) {
		tmp = a * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if t <= -1.9e+48:
		tmp = t_1
	elif t <= -1.05e-48:
		tmp = y * (x * z)
	elif t <= 2.65e+45:
		tmp = a * (b * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (t <= -1.9e+48)
		tmp = t_1;
	elseif (t <= -1.05e-48)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 2.65e+45)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	tmp = 0.0;
	if (t <= -1.9e+48)
		tmp = t_1;
	elseif (t <= -1.05e-48)
		tmp = y * (x * z);
	elseif (t <= 2.65e+45)
		tmp = a * (b * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+48], t$95$1, If[LessEqual[t, -1.05e-48], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.65e+45], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9e48 or 2.64999999999999996e45 < t

   1. Initial program 59.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 59.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 59.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 59.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 59.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 59.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 59.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 59.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 59.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 49.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 49.1%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 49.1%

         \[\leadsto \left(-\color{blue}{\left(t \cdot x\right) \cdot a}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. distribute-rgt-neg-in 49.1%

         \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 49.1%

      \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in c around inf 43.1%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -1.9e48 < t < -1.04999999999999994e-48

   1. Initial program 69.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 69.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 69.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 69.8%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 69.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 69.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 69.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 69.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 44.3%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in y around inf 32.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -1.04999999999999994e-48 < t < 2.64999999999999996e45

   1. Initial program 79.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 79.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 80.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 80.7%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 80.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 80.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 80.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 80.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 64.9%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in i around inf 37.1%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+48}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+45}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 21: 30.4% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-48} \lor \neg \left(t \leq 8.8 \cdot 10^{+45}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.05e-48) (not (<= t 8.8e+45))) (* c (* t j)) (* a (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.05e-48) || !(t <= 8.8e+45)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-1.05d-48)) .or. (.not. (t <= 8.8d+45))) then
        tmp = c * (t * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.05e-48) || !(t <= 8.8e+45)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -1.05e-48) or not (t <= 8.8e+45):
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.05e-48) || !(t <= 8.8e+45))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -1.05e-48) || ~((t <= 8.8e+45)))
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.05e-48], N[Not[LessEqual[t, 8.8e+45]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.04999999999999994e-48 or 8.8000000000000001e45 < t

   1. Initial program 61.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 61.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 61.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 61.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 61.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 61.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 61.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 61.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 61.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in t around inf 50.6%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 50.6%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 50.6%

         \[\leadsto \left(-\color{blue}{\left(t \cdot x\right) \cdot a}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. distribute-rgt-neg-in 50.6%

         \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 50.6%

      \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in c around inf 37.7%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -1.04999999999999994e-48 < t < 8.8000000000000001e45

   1. Initial program 79.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 79.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 80.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 80.7%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 80.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 80.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 80.7%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 80.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 64.9%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in i around inf 37.1%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-48} \lor \neg \left(t \leq 8.8 \cdot 10^{+45}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 22: 22.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (b * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.8%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Step-by-step derivation

   1. +-commutative 69.8%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

   2. fma-def 71.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

   3. *-commutative 71.4%

      \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   4. *-commutative 71.4%

      \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

   5. *-commutative 71.4%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

   6. *-commutative 71.4%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

3. Simplified 71.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

4. Taylor expanded in j around 0 59.3%

   \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

5. Taylor expanded in i around inf 23.0%

   \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

6. Final simplification 23.0%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Developer target: 69.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2023173 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))